What are the length and width of a rectangular

traffic sign if the length exceeds the width by 6

inches and the perimeter is 112inches?

width is 25 inches

length is 31 inches

Step-by-step explanation:

We will need the formula for perimeter of a rectangle:

P = 2 (l + w)

"l" is length, "w" is width

If the length exceeds the width by 6, then:

l = w + 6 < = Substitute this into the equation

P = 2 (l + w)

P = 2 (w + 6 + w)

Remember we also know the perimeter is 112:

112 = 2 (w + 6 + w)

Collect like terms:

112 = 2 (2w + 6)

Start isolating "w" to find width.

56 = 2w + 6 Divided both sides by 2

50 = 2w Subtracted 6 from both sides

25 = w Divided both sides by 2

w = 25 Variable on left for standard formatting

The width is 25 inches.

Find the length using "length exceeds width by 6".

l = w + 6

l = 25 + 6 Substitute the width

l = 31

The length is 31 inches.

∴ The length is 31 inches and the width is 25 inches.

Check your answer with the perimeter formula.

P = 2 (l + w)

112 = 2 (31 + 25) Substitute all the variables.

112 = 2 (56)

112 = 112 Same answer

LS = RS Left side equals right side

The answer is correct.